450 RILEY [CHAP. 20 



shown in Fig. 4b. The family simulates vertical distributions that have often 

 been observed in nature, where summer conditions correspond to low values 

 of A and winter distributions are simulated by strong mixing. The maximum 

 population is attained with an intermediate mixing rate. With strong turbu- 

 lence, plankton is rapidly removed from the lower part of the productive layer, 

 so that the largest population occurs near the surface. When the diffusion co- 

 efficient is low, the surface water is depleted by sinking, and a maximum is 

 attained in the lower part of the productive layer. Some investigators have 

 postulated that this type of distribution is due to increasing density and 

 decreasing sinking rate near the bottom of the euphotic zone. The model 

 shows that this is not necessarily so. However, Steele and Yentsch (1960) 

 have pointed out that the maximum sometimes occurs below the limit of the 

 euphotic zone, and they are correct in stating that this requires a reduction in 

 sinking rate if it is to be a stable, continuing situation. 



Steele (1958) has used an idealized two-layered system to good effect in 

 simple equations that may be used either for steady-state determinations or 

 time sequences. In his model the thermocline has a fixed depth, and the layers 

 above and below are postulated to be homogeneous with respect to all variables. 

 A simple mixing coefficient is postulated, consisting of a daily exchange of a 

 fraction of the water across the boundary between the two layers. Similarly, 

 phytoplankton sinking is represented by a daily transfer of a constant fraction 

 of the population from the upper layer to the lower one. 



Phytoplankton production is assumed to be linearly proportional to phos- 

 phate when the latter is less than 0.4 y.g atom P/l. and independent at higher 

 concentrations. No other environmental variables were introduced into the 

 production coefficient. The phosphate concentration is postulated to depend 

 upon phytoplankton growth and is independent of zooplankton. The rather 

 difficult problems of zooplankton growth and loss were by-passed by deriving 

 suitable constants from observed seasonal changes on Fladen Ground. In a 

 case where the depth of the surface layer is 40 m, and phosphate is less than 

 0.4 [xg atoms P/l., the equations for this layer are 



% = (0.75w-0.11-0.024/i-m)p, (22) 



at 



fit) 



ZZ = _(0.58w- 0.021)p + m(0.70-n). (23) 



^ = 4?j-0.0U 2 , (24) 



where p is phytoplankton, n phosphate, h herbivores, and m is the mixing 

 coefficient. The constant in (22), —0.11, includes a term for phytoplankton 

 respiration derived from (7) and also a term for loss by sinking based on an 

 estimated sinking rate of 3 m/day. The first term on the right-hand side of (23) 

 is derived from — (pn — r)vp, as previously postulated in (13). The right-hand 

 term assumes that phosphate in the lower layer is constant at 0.70 y.g atom. 



